The field of the invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to the sampling of acquired NMR signals at prescribed sample rates.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B.sub.0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B.sub.1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, M.sub.z, may be rotated, or "tipped", into the x-y plane to produce a net transverse magnetic moment M.sub.t. A signal is emitted by the excited spins after the excitation signal B.sub.1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (G.sub.x G.sub.y and G.sub.z) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
The rate at which the received NMR signals are digitized is an important scan parameter. The signal-to-noise ratio of an NMR image can be improved if the effective bandwidth (which is the inverse of the sampling period per point) is reduced. This is usually accomplished by widening the read-out gradient pulse and reducing the amplitude of the read-out gradient to encode the positions into a narrower bandwidth and to retain the same spatial resolution. The anti-aliasing filters are modified to match the reduced bandwidth and the analog-to-digital conversion (A/D) sample rate is reduced to acquire the same number of samples over the longer read-out gradient pulse. The SNR improvement is proportional to the square root of the bandwidth reduction.
A higher SNR and corresponding lower A/D sample rate is not always desired, since the increase in SNR is accompanied by two disadvantages. First, the minimum echo delay (TE.sub.1 min) for the first NMR echo signal is increased due to the widening of the read-out gradient pulse. For some rf spin echo acquisitions the delay is twice what might be expected, since the time between the 90.degree. RF excitation pulse and the 180.degree. RF pulse must also be increased to orient the NMR echo signal at the center of the widened read-out gradient pulse. The lengthening of TE.sub.1 is a disadvantage when T.sub.2 weighting of the NMR image is not desired. A second disadvantage which accompanies this increase in SNR is an increase in chemical shift artifacts. Since the bandwidth per image pixel is reduced, the frequency difference between lipid and water resonances becomes more significant. For example, at 1.5 Tesla main field strength, the approximately 220 Hertz difference in resonant frequency will appear approximately three times further apart in an image where each image pixel represents a difference in frequency of 42 Hertz rather than 125 Hertz. The result is an increased relative displacement between the lipid structures and the water structures. This displacement can be especially disturbing with images reconstructed from the first NMR echo signal since the second echo signal often has lower lipid signal components due to the shorter T.sub.2 decay time of lipids.
To allow maximum flexibility of the SNR, spatial resolution, and field of view of an image, a completely adjustable A/D sampling rate is desirable.
A number of methods have been used in prior MRI systems to enable the A/D sample rate to be precisely adjusted to enable the best image acquisition possible. One approach is to employ an analog-to-digital converter circuit ("ADC") in which the sample rate is adjustable and can be precisely controlled. Such ADCs are expensive.
Another approach is to employ an ADC which has a fixed sample rate far higher than that required to achieve the desired sample rates. In such designs the sample rate is reduced to the prescribed A/D sample rate by using decimation. The decimation ratio (d) is an integer value. Decimation effectively reduces the A/D sample rate to one-half (d=2) by selecting alternate digitized samples, to one-third (d=3) by selecting every third digitized sample, to one-fourth (d=4) by selecting every fourth digitized sample, etc. The difficulty with this method is that the effective A/D sample rate can only be changed in discrete steps. If the ADC sample rate is very high and the decimation ratio (d) necessary to achieve operable A/D sample rates is very high (e.g. d=10, 11, 12), these discrete steps are relatively small and a desired A/D sample rate can be achieved with reasonable accuracy. However, ADC devices that operate at such high sample rates are expensive.
Another known method for decimating a signal sampled at a high sample rate is to Fourier transform the signal, filter out the high frequency components and Fourier transform the filtered frequency domain signal back to the time domain. While straight forward in principle, this method is impractical because discrete Fourier transforms ("DFT") are required and these take too much time to perform on the large image data sets employed in MRI systems.